Let R1 and R2 be two relations defined on a non empty set A- Which of the following statements is false- Give reasons in support of your answer-a If R1 and R2 are reflexive- then so is R1- R2b If R1 and R2 are symmetric- then so is R1- R2c If R1 and R2 are transitive- then so is R1- R2d If R1 and R2 are transitive- then so is R1- R2e If R1 and R2 are symmetric- then so is R1- R2

(a) True, for all x∈ A, (x, x)∈ R_1 and (x, x)∈ R_2⇒ (x, x)∈ R_1∩ R_2 .(b) True; (x, y)∈ R_1∪ R_2⇒ (x, y)∈ R_1 #160;or #160;(x, y)∈ R_2⇒ (y ...

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Reflexive Relations

Let R1 and ...

Question

Let $R_{1}$ and $R_{2}$ be two relations defined on a non empty set A. Which of the following statements is false? Give reasons in support of your answer.
(a) If $R_{1}$ and $R_{2}$ are reflexive, then so is $R_{1} \cap R_{2}$
(b) If $R_{1}$ and $R_{2}$ are symmetric, then so is $R_{1} \cup R_{2}$
(c) If $R_{1}$ and $R_{2}$ are transitive, then so is $R_{1} \cup R_{2}$
(d) If $R_{1}$ and $R_{2}$ are transitive, then so is $R_{1} \cap R_{2}$
(e) If $R_{1}$ and $R_{2}$ are symmetric, then so is $R_{1} \cap R_{2}$

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